\(a.x+\left(x-1\right)+\left(x-2\right)+...+\left(x-100\right)=110x+8\)

\(\Leftrightarrow101x-\left(1+2+...+100\right)=110x+8\)

\(\Leftrightarrow101x-\frac{100\left(100+1\right)}{2}=110x+8\)

\(\Leftrightarrow101x-5050=110x+8\)

\(\Leftrightarrow101x-110x=8+5050\)

\(\Leftrightarrow-9x=5058\)

\(\Leftrightarrow x=5058\div\left(-9\right)\)

\(\Leftrightarrow x=-562\)

\(b.3x-7x+11x-15x+...+155x-159x=1680\)

\(\Leftrightarrow\left(3x-7x\right)+\left(11x-15x\right)+...+\left(155x-159x\right)=1680\)

\(\Leftrightarrow-4x-4x-...-4x=1680\)

\(\Leftrightarrow-80x=1680\)

\(\Leftrightarrow x=1680\div\left(-80\right)\)

\(\Leftrightarrow x=-21\)

1: 7-x=8+(-7)

=>7-x=8-7=1

=>x=7-1=6

2: \(x-8=\left(-3\right)-8\)

=>x-8=-11

=>\(x=-11+8=-3\)

3: \(2-x=10-9+23\)

=>\(2-x=33-9=24\)

=>x=2-24=-22

4: \(-2-x=15\)

=>\(x=-2-15=-17\)

5: \(-7+x-8=-3-1+13\)

=>x-14=13-4=9

=>x=9+14=23

6: 100-x+7=-x+3

=>107-x=3-x

=>107=3(vô lý)

7: \(23+x=8-2x\)

=>\(x+2x=8-23\)

=>3x=-15

=>x=-15/3=-5

cảm ơn bạn

a) \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=5750\)

\(\Rightarrow\left(x+x+x+...+x\right)+\left(1+2+3+..+100\right)=5750\Rightarrow x.100+\left(100+1\right)\cdot100:2=5750\)\

\(\Rightarrow x.100+5050=5750\Rightarrow x.100=700\Rightarrow x=7\)

b) \(\frac{x+1}{2}=\frac{8}{x+1}\Rightarrow\left(x+1\right)\left(x+1\right)=2.8\)

\(\Rightarrow\left(x+1\right)^2=16\Rightarrow\left(x+1\right)^2=4^2\)

\(\Leftrightarrow x+1=4\Rightarrow x=3\)

1.\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=5750\)

\(\Leftrightarrow\left(x+x+x+...+x\right)+\left(1+2+3+...+100\right)=5750\)

\(\Leftrightarrow100x+5050=5750\)

\(\Leftrightarrow100x=5750-5050=700\)

\(\Leftrightarrow x=700:100=7\)

2.   \(\frac{x+1}{2}=\frac{8}{x+1}\)

\(\Leftrightarrow\left(x+1\right).\left(x+1\right)=8.2\)

\(\Leftrightarrow\left(x+1\right).\left(x+1\right)=16\)

\(\Leftrightarrow\left(x+1\right)^2=16\)

\(\Leftrightarrow\left(x+1\right)=16:2\)

\(\Leftrightarrow\left(x+1\right)=8\)

\(\Leftrightarrow x=8-1=7\)

2/ 1 - 3 + 5 - 7 + ... + (x-2) - x = -600

=> ( - 2 ) + ( - 2 ) + .... + ( - 2 ) = - 600 ( số số hạng các số - 2 là A ) 

=> ( - 2 ) . A =  - 600 => A = 300 

Mặt Khác số số hạng ở dãy trên = ( x - 1 ) : 2 + 1 ( 1 ) 

Số số cặp = Số số hạng : 2 = 300 => Số số hạng = 600 

Thay vào ( 1 ) Ta có :

( x - 1 ) : 2 + 1 = 600 => ( x - 1 ) : 2 = 599 => x = 599 . 2 + 1 = 1198+ 1 = 1199 

Các câu 1,3,4 làm tương tự

2+4+6+..........+x=600

a) \(???\)

b) \(123x+877x=2000\)

     \(1000x=2000\)

      \(x=2000:1000\)

      \(x=2\)

c) \(2x.\left(x-10\right)=0\)

    => \(x-10=0\)

         \(x=10\)

d)\(6.\left(x+2\right)-\left(4x+10\right)=100\)

    \(6.x+12-4x+10=100\)

     \(2x+2=100\)

     \(2x=98\)

     \(x=98:2\)

     \(x=49\)

e) \(x.\left(x+1\right)=2+4+6+8+...+2500\)

     \(x.\left(x+1\right)=1563750\)

      mà ta thấy : \(1250.1251=1563750\)

=> \(x=1250\)

g)\(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5750\)

     \(x.100+5050=5750\)

     \(x.100=5750-5050\)

     \(x.100=700\)

     \(x=7\)

Ko chép đề

\(2)x-17+x=x-7\)

\(x+x-x=-7+17\)

\(x=-10\)

Vậy ....

âm 10 , nhỉ ?